Planetarium domes and domes for projection of other types of displays have evolved in the prior art from relatively small structures composed of individual self-supporting segmented panels to much larger structures wherein a frame and intermediate support structure must be provided for the individual panels of the dome. Techniques have been developed for producing screen segments and desired curvatures which are designed to be fitted together with a high degree of precision. However, supports for such screens have often been unsatisfactory from a standpoint of the precision desired in achieving a predetermined curvature and in any event have been awkward and difficult to build. In particular, dome support constructions which have been fabricated as a gridwork of structural numbers are themselves difficult to fit together and often very difficult to interconnect at junctions using conventional fastening means. Moreover, distortions in the screen surface may result from trying to conform the screen too closely to a support frame structure. Either the support structure is not built to conform sufficiently closely to the screen shape so that distortion occurs in attempting to make the screen conform, or the support structure is built in such a way that the support pieces themselves do not fit together properly so that the screen cannot conform to the support, or the screen pieces will not be adequately supported on the frame.